The Transmuted Marshall-Olkin Power Distribution: Estimations and Applications

In this study, we introduce and develop a new flexible distribution called the Transmuted Marshall-Olkin Power distribution the work not only presents the new distribution but also comprehensively derives its mathematical and structural properties, including moments, the moment generating function, the characteristic function, quantile function and order statistics.

The problem of estimating the distribution parameters was addressed by comparing the performance of two different estimation methods: the maximum likelihood method and the least square method. For an objective comparison between these methods, we relied on an extensive simulation study using the criteria of Bias and Mean Square Error as key measures of accuracy and efficiency.

The simulation results demonstrated conclusively that the least square method performed best and was the most efficient for estimating the parameters of the proposed distribution compared to the other.

The efficiency, importance and flexibility of the Transmuted Marshall-Olkin Power distribution were demonstrated through applications to real dataset. Several goodness-of-fit statistics were employed, including the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Corrected Akaike Information Criterion(AICC) and Consistent Akaike Information Criterion (CAIC), In addition to the log-likelihood function evaluated at the maximum likelihood estimates (-2l ̂) . the comparative analysis revealed that the proposed TMOP distribution consistently achieved lower information criteria value than the competing models, confirming its superior fitting capability, robustness and flexibility. Therefore, the TMOP distribution can be considered a promising alternative for modeling a wide variety of real-world data.